메뉴 건너뛰기




Volumn 64, Issue 2, 2011, Pages 161-182

Necessary and sufficient conditions for linear convergence of ℓ1-regularization

Author keywords

[No Author keywords available]

Indexed keywords


EID: 78449233271     PISSN: 00103640     EISSN: 00103640     Source Type: Journal    
DOI: 10.1002/cpa.20350     Document Type: Article
Times cited : (143)

References (37)
  • 1
    • 74849124067 scopus 로고    scopus 로고
    • Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators
    • Anzengruber, S. W.; Ramlau, R. Morozov's discrepancy principle for Tikhonov-type functionals with nonlinear operators. Inverse Problems 26 ( 2010), no. 2, 025001, 17 pp.
    • (2010) Inverse Problems , vol.26 , Issue.2 , pp. 17
    • Anzengruber, S.W.1    Ramlau, R.2
  • 2
    • 0004099213 scopus 로고    scopus 로고
    • Optima and equilibria. An introduction to nonlinear analysis
    • 2nd ed. Graduate Texts in Mathematics, 140., Springer, Berlin
    • Aubin, J.-P. Optima and equilibria. An introduction to nonlinear analysis. 2nd ed. Graduate Texts in Mathematics, 140. Springer, Berlin, 1998.
    • (1998)
    • Aubin, J.1
  • 3
    • 0003478998 scopus 로고
    • Nonlinear semigroups and differential equations in Banach spaces
    • Editura Academiei Republicii Socialiste România, Bucharest;, Noordhoff, Leiden, The Netherlands
    • Barbu, V. Nonlinear semigroups and differential equations in Banach spaces. Editura Academiei Republicii Socialiste România, Bucharest; Noordhoff, Leiden, The Netherlands, 1976.
    • (1976)
    • Barbu, V.1
  • 4
    • 62649147819 scopus 로고    scopus 로고
    • Morozov's discrepancy principle and Tikhonov-type functionals
    • Bonesky, T. Morozov's discrepancy principle and Tikhonov-type functionals. Inverse Problems 25 ( 2009), no. 1, 015015, 11 pp.
    • (2009) Inverse Problems , vol.25 , Issue.1 , pp. 11
    • Bonesky, T.1
  • 5
    • 57349100926 scopus 로고    scopus 로고
    • Linear convergence of iterative soft-thresholding
    • Bredies, K.; Lorenz, D. A. Linear convergence of iterative soft-thresholding. J. Fourier Anal. Appl. 14 ( 2008), no. 5-6, 813-837.
    • (2008) J. Fourier Anal. Appl. , vol.14 , Issue.5-6 , pp. 813-837
    • Bredies, K.1    Lorenz, D.A.2
  • 6
    • 6444243748 scopus 로고    scopus 로고
    • Convergence rates of convex variational regularization
    • Burger, M.; Osher, S. Convergence rates of convex variational regularization. Inverse Problems 20 ( 2004), no. 5, 1411-1421.
    • (2004) Inverse Problems , vol.20 , Issue.5 , pp. 1411-1421
    • Burger, M.1    Osher, S.2
  • 7
    • 77955509952 scopus 로고    scopus 로고
    • Shifting inequality and recovery of sparse signals
    • Cai, T.; Wang, L.; Xu, G. Shifting inequality and recovery of sparse signals. IEEE Trans. Signal Process. 58 ( 2010), no. 3, 1300-1308.
    • (2010) IEEE Trans. Signal Process , vol.58 , Issue.3 , pp. 1300-1308
    • Cai, T.1    Wang, L.2    Xu, G.3
  • 9
    • 42649140570 scopus 로고    scopus 로고
    • The restricted isometry property and its implications for compressed sensing
    • Candès, E. J. The restricted isometry property and its implications for compressed sensing. C. R. Math. Acad. Sci. Paris 346 ( 2008), no. 9-10, 589-592.
    • (2008) C. R. Math. Acad. Sci. Paris , vol.346 , Issue.9-10 , pp. 589-592
    • Candès, E.J.1
  • 10
    • 31744440684 scopus 로고    scopus 로고
    • Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
    • Candès, E. J.; Romberg, J.; Tao, T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inform. Theory 52 ( 2006), no. 2, 489-509.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.2 , pp. 489-509
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 11
    • 33745604236 scopus 로고    scopus 로고
    • Stable signal recovery from incomplete and inaccurate measurements
    • Candès, E. J.; Romberg, J.; Tao, T. Stable signal recovery from incomplete and inaccurate measurements. Comm. Pure Appl. Math. 59 ( 2006), no. 8, 1207-1223.
    • (2006) Comm. Pure Appl. Math. , vol.59 , Issue.8 , pp. 1207-1223
    • Candès, E.J.1    Romberg, J.2    Tao, T.3
  • 12
    • 29144439194 scopus 로고    scopus 로고
    • Decoding by linear programming
    • Candès, E. J.; Tao, T. Decoding by linear programming. IEEE Trans. Inform. Theory 51 ( 2005), no. 12, 4203-4215.
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.12 , pp. 4203-4215
    • Candès, E.J.1    Tao, T.2
  • 13
    • 0003603616 scopus 로고
    • Geometry of Banach spaces, duality mappings and nonlinear problems
    • Mathematics and Its Applications, 62., Kluwer, Dordrecht, The Netherlands
    • Cioranescu, I. Geometry of Banach spaces, duality mappings and nonlinear problems. Mathematics and Its Applications, 62. Kluwer, Dordrecht, The Netherlands, 1990.
    • (1990)
    • Cioranescu, I.1
  • 14
    • 7044231546 scopus 로고    scopus 로고
    • An iterative thresholding algorithm for linear inverse problems with a sparsity constraint
    • Daubechies, I.; Defrise, M.; De Mol, C. An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Comm. Pure Appl. Math. 57 ( 2004), no. 11, 1413-1457.
    • (2004) Comm. Pure Appl. Math. , vol.57 , Issue.11 , pp. 1413-1457
    • Daubechies, I.1    Defrise, M.2    De Mol, C.3
  • 16
    • 33144483155 scopus 로고    scopus 로고
    • Stable recovery of sparse overcomplete representations in the presence of noise
    • Donoho, D. L.; Elad, M.; Temlyakov, V. N. Stable recovery of sparse overcomplete representations in the presence of noise. IEEE Trans. Inform. Theory 52 ( 2006), no. 1, 6-18.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.1 , pp. 6-18
    • Donoho, D.L.1    Elad, M.2    Temlyakov, V.N.3
  • 17
    • 0343650333 scopus 로고
    • Maximum entropy regularization for Fredholm integral equations of the first kind
    • Eggermont, P. P. B. Maximum entropy regularization for Fredholm integral equations of the first kind. SIAMJ. Math. Anal. 24 ( 1993), no. 6, 1557-1576.
    • (1993) SIAMJ. Math. Anal. , vol.24 , Issue.6 , pp. 1557-1576
    • Eggermont, P.P.B.1
  • 18
    • 0003244186 scopus 로고
    • Convex analysis and variational problems
    • North-Holland, Amsterdam-Oxford;, Elsevier, New York
    • Ekeland, I.; Temam, R. Convex analysis and variational problems. Studies in Mathematics and Its Applications, 1. North-Holland, Amsterdam-Oxford; Elsevier, New York, 1976.
    • (1976) Studies in Mathematics and Its Applications, 1
    • Ekeland, I.1    Temam, R.2
  • 22
    • 26844461512 scopus 로고    scopus 로고
    • Recovery of exact sparse representations in the presence of bounded noise
    • Fuchs, J. J. Recovery of exact sparse representations in the presence of bounded noise. IEEE Trans. Inform. Theory 51 ( 2005), no. 10, 3601-3608.
    • (2005) IEEE Trans. Inform. Theory , vol.51 , Issue.10 , pp. 3601-3608
    • Fuchs, J.J.1
  • 24
    • 78449232078 scopus 로고    scopus 로고
    • The residual method for regularizing ill-posed problems. Reports of FSP S105 "Photoacoustic Imaging" 14, University of Innsbruck, Austria, arXiv:0905.1187v1
    • Grasmair, M.; Haltmeier, M.; Scherzer, O. The residual method for regularizing ill-posed problems. Reports of FSP S105 "Photoacoustic Imaging" 14, University of Innsbruck, Austria, 2009. arXiv:0905.1187v1.
    • (2009)
    • Grasmair, M.1    Haltmeier, M.2    Scherzer, O.3
  • 25
    • 70350327168 scopus 로고    scopus 로고
    • Approximate source conditions for nonlinear ill-posed problems-chances and limitations
    • Hein, T.; Hofmann, B. Approximate source conditions for nonlinear ill-posed problems-chances and limitations. Inverse Problems 25 ( 2009), no. 3, 035003, 16 pp.
    • (2009) Inverse Problems , vol.25 , Issue.3 , pp. 16
    • Hein, T.1    Hofmann, B.2
  • 26
    • 34249721452 scopus 로고    scopus 로고
    • A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators
    • Hofmann, B.; Kaltenbacher, B.; Pöschl, C.; Scherzer, O. A convergence rates result for Tikhonov regularization in Banach spaces with non-smooth operators. Inverse Problems 23 ( 2007), no. 3, 987-1010.
    • (2007) Inverse Problems , vol.23 , Issue.3 , pp. 987-1010
    • Hofmann, B.1    Kaltenbacher, B.2    Pöschl, C.3    Scherzer, O.4
  • 27
    • 0004146405 scopus 로고    scopus 로고
    • Theory of linear ill-posed problems and its applications
    • 2nd ed. Translated and revised from the 1978 Russian original ["Nauka", Moscow; MR0511653]. Inverse and Ill-Posed Problems Series., VSP, Utrecht
    • Ivanov, V. K.; Vasin, V. V.; Tanana, V. P. Theory of linear ill-posed problems and its applications. 2nd ed. Translated and revised from the 1978 Russian original ["Nauka", Moscow; MR0511653]. Inverse and Ill-Posed Problems Series. VSP, Utrecht, 2002.
    • (2002)
    • Ivanov, V.K.1    Vasin, V.V.2    Tanana, V.P.3
  • 28
    • 51749124719 scopus 로고    scopus 로고
    • Convergence rates and source conditions for Tikhonov regularization with sparsity constraints
    • Lorenz, D. A. Convergence rates and source conditions for Tikhonov regularization with sparsity constraints. J. Inverse Ill-Posed Probl. 16 ( 2008), no. 5, 463-478.
    • (2008) J. Inverse Ill-Posed Probl. , vol.16 , Issue.5 , pp. 463-478
    • Lorenz, D.A.1
  • 29
    • 70350330305 scopus 로고    scopus 로고
    • On enhanced convergence rates for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces
    • Neubauer, A. On enhanced convergence rates for Tikhonov regularization of nonlinear ill-posed problems in Banach spaces. Inverse Problems 25 ( 2009), no. 6, 065009, 10 pp.
    • (2009) Inverse Problems , vol.25 , Issue.6 , pp. 10
    • Neubauer, A.1
  • 30
    • 78449236353 scopus 로고    scopus 로고
    • Convergence rates for regularization with sparsity constraints
    • Ramlau, R.; Resmerita, E. Convergence rates for regularization with sparsity constraints. Electron. Trans. Numer. Anal. 37 ( 2010), 87-104.
    • (2010) Electron. Trans. Numer. Anal. , vol.37 , pp. 87-104
    • Ramlau, R.1    Resmerita, E.2
  • 31
    • 23244453192 scopus 로고    scopus 로고
    • Regularization of ill-posed problems in Banach spaces: convergence rates
    • Resmerita, E. Regularization of ill-posed problems in Banach spaces: convergence rates. In verse Problems 21 ( 2005), no. 4, 1303-1314.
    • (2005) In verse Problems , vol.21 , Issue.4 , pp. 1303-1314
    • Resmerita, E.1
  • 32
    • 33744766866 scopus 로고    scopus 로고
    • Error estimates for non-quadratic regularization and the relation to enhancement
    • Resmerita, E.; Scherzer, O. Error estimates for non-quadratic regularization and the relation to enhancement. Inverse Problems 22 ( 2006), no. 3, 801-814.
    • (2006) Inverse Problems , vol.22 , Issue.3 , pp. 801-814
    • Resmerita, E.1    Scherzer, O.2
  • 33
    • 0035427533 scopus 로고    scopus 로고
    • A posteriori error estimates for the solution of nonlinear ill-posed operator equations
    • Ser. A: Theory Methods
    • Scherzer, O. A posteriori error estimates for the solution of nonlinear ill-posed operator equations. Nonlinear Anal. 45 ( 2001), no. 4, Ser. A: Theory Methods, 459-481.
    • (2001) Nonlinear Anal. , vol.45 , Issue.4 , pp. 459-481
    • Scherzer, O.1
  • 34
    • 85067915677 scopus 로고    scopus 로고
    • Variational methods in imaging
    • Applied Mathematical Sciences, 167., Springer, New York
    • Scherzer, O.; Grasmair, M.; Grossauer, H.; Haltmeier, M.; Lenzen, F. Variational methods in imaging. Applied Mathematical Sciences, 167. Springer, New York, 2009.
    • (2009)
    • Scherzer, O.1    Grasmair, M.2    Grossauer, H.3    Haltmeier, M.4    Lenzen, F.5
  • 35
    • 78449263886 scopus 로고    scopus 로고
    • Methods for solution of nonlinear operator equations
    • VSP, Utrecht
    • Tanana, V. P. Methods for solution of nonlinear operator equations. Inverse and Ill-Posed Problems Series. VSP, Utrecht, 1997.
    • (1997) Inverse and Ill-Posed Problems Series
    • Tanana, V.P.1
  • 36
    • 33645712308 scopus 로고    scopus 로고
    • Just relax: convex programming methods for identifying sparse signals in noise
    • Tropp, J. A. Just relax: convex programming methods for identifying sparse signals in noise. IEEE Trans. Inform. Theory 52 ( 2006), no. 3, 1030-1051.
    • (2006) IEEE Trans. Inform. Theory , vol.52 , Issue.3 , pp. 1030-1051
    • Tropp, J.A.1
  • 37
    • 0003435748 scopus 로고    scopus 로고
    • A review of posteriori error estimation & adaptive mesh-refinement techniques
    • Wiley, Chichester
    • Verfürth, R. A review of posteriori error estimation & adaptive mesh-refinement techniques. Wiley, Chichester, 1996.
    • (1996)
    • Verfürth, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.